Susceptible $$\frac{dS}{dt} = - \frac{\beta I S}{N} + \omega R$$
Exposed $$\frac{dE}{dt} = \frac{\beta I S}{N} - \sigma E$$
Infecitous $$\frac{dI}{dt} = \sigma E - \gamma I$$
Removed $$\frac{dR}{dt} = \gamma I - \omega R$$
Reproductive ratio $$R_0 = \frac{\beta \sigma}{(\gamma+\mu) (\mu \sigma)}$$